Related papers: On pseudosymmetric manifolds
We prove that Riemannian metrics with an absolute Ricci curvature bound and a conjugate radius bound can be smoothed to having a sectional curvature bound. Using this we derive a number of results about structures of manifolds with Ricci…
In this paper, we give various curvature pinching conditions such that shrinkers are compact. On one hand, we prove that shrinkers with positive Ricci curvature are compact when they have bounded curvature and certain curvature pinching…
In this paper, we shall give a new upper diameter estimate for complete Riemannian manifolds in the case that the Bakry-\'Emery Ricci curvature has a positive lower bound and the norm of the potential function has an upper bound. Our…
The purpose of this report is to acknowledge the influence of M. Gromov's vision of geometry on our own works. It is two-fold: in the first part we aim at describing some results, in dimension 3, around the question: which open 3-manifolds…
We consider Minkowski compactifications of M-theory on generic seven-dimensional manifolds. After analyzing the conditions on the four-form flux, we establish a set of relations between the components of the intrinsic torsion of the…
In a series of papers, Bamler [Bam20a,Bam20b,Bam20c] further developed the high-dimensional theory of Hamilton's Ricci flow to include new monotonicity formulas, a completely general compactness theorem, and a long-sought partial regularity…
In this paper, we consider the rigidity for an $n(\geq 4)$-dimensional submanfolds $M^n$ with parallel mean curvature in the space form ${\mathbb M}^{n+p}_c$ when the integral Ricci curvature of $M$ has some bound. We prove that, if…
We provide new type of decay estimate for scalar curvatures of steady gradient Ricci solitons. We also give certain upper bound for the diameter of a Riemannian manifold whose $\infty$-Bakry--Emery Ricci tensor is bounded by some positive…
We show that a compact Riemannian manifold with weakly 1/4-pinched sectional curvatures is either locally symmetric or diffeomorphic to a space form.
We determine the most general near-horizon geometry of a supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional minimal gauged supergravity that admits two rotational symmetries. The near-horizon geometry is…
In this paper, we study two notions of rigidity, one of conformal submersions and the other of quasi Einstein manifolds, with an attempt to relate the two notions. Note that a smooth submersion between Riemannian manifolds is called…
In this paper, we consider the scalar curvature in the distributional sense of \cite{MR3366052} and the scalar curvature lower bound in the $\beta-$weak $(\beta\in(0, \frac{1}{2}))$ sense of \cite{MR4685089} on an asymptotically flat…
A conformal transformation of a semi-Riemannian manifold is essential if there is no conformally equivalent metric for which it is an isometry. For Riemannian manifolds the existence of an essential conformal transformation forces the…
Along the line of the Yang Conjecture, we give a new estimate on the lower bound of the first non-zero eigenvalue of a closed Riemannian manifold with negative lower bound of Ricci curvature in terms of the in-diameter and the lower bound…
The object of this paper is study $(\epsilon)$-para-Sasakian 3-manifolds satisfying certain conditions on the $\mathcal{Z}$ tensor. We characterize, $\mathcal{Z}$-symmetric; $\mathcal{Z}$-semisymmetric; $\mathcal{Z}$-pseudosymmetric; and…
This paper introduces even triangulations of n-dimensional pseudo-manifolds and links their combinatorics to the topology of the pseudo-manifolds. This is done via normal hypersurface theory and the study of certain symmetric…
Weighted quadratic estimates are proved for certain bisectorial firstorder differential operators with bounded measurable coefficients which are (not necessarily pointwise) accretive, on complete manifolds with positive injectivity radius.…
We propose a generalization of pseudospin and spin symmetries, the SU(2) symmetries of Dirac equation with scalar and vector mean-field potentials originally found independently in the 70's by Smith and Tassie, and Bell and Ruegg. As…
In this paper we study some splitting properties on complete noncompact manifolds with smooth measures when $\infty$-dimensional Bakry-\'Emery Ricci curvature is bounded from below by some negative constant and spectrum of the weighted…
Verifying a conjecture of Gromov we establish a generalized Margulis Lemma for manifolds with lower Ricci curvature bound. Among the various applications are finiteness results for fundamental groups of compact $n$-manifolds with upper…